A local paint store carries 4 brands of paint (W, X, Y, and Z). The store has 5 cans of W, 3 cans of X, 6 cans of Y, and 15 cans of Z, all in white. It is thought that customers have no preference for one of these brands over another. If this is the case, what is the probability that the next 5 customers will select 1 can of W, X, Y and 2 cans of brand Z?
A) About .23
B) Approximately .08
C) Over .30
D) 0.25

Question

Quizplus · Accepted Answer

The probability of selecting 1 can of W, X, Y, and 2 cans of Z out of the total cans available can be calculated using the combination formula and the principle of probability. The total number of cans is 5 (W) + 3 (X) + 6 (Y) + 15 (Z) = 29 cans. The probability of selecting these specific cans in any order is calculated by multiplying the probabilities of selecting each can:- For W: 5/29 (since there are 5 W cans out of 29 total cans)- For X: 3/28 (after one can is taken, there are 28 cans left, and 3 of them are X)- For Y: 6/27 (after two cans are taken, there are 27 cans left, and 6 of them are Y)- For the first Z: 15/26 (after three cans are taken, there are 26 cans left, and 15 of them are Z)- For the second Z: 14/25 (after four cans are taken, including one Z, there are 25 cans left, and 14 of them are Z)The probability of this specific sequence happening is the product of these probabilities. However, since the order in which the cans are selected doesn't matter, we must also consider the combinations of selecting these cans, which adds complexity to the calculation. The correct answer, therefore, accounts for both the selection probabilities and the combinations, leading to an approximation rather than a straightforward calculation from the probabilities given above. The exact calculation involves more detailed combinatorial analysis, but the approximation given in the choices suggests a relatively low probability, consistent with the complexity and specificity of the event described.

A Local Paint Store Carries 4 Brands of Paint (W